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A financial planner has three portfolios: A, B, and C. Because investors have different tolerances for risks, 20% of people are likely to invest in portfolio A, 30% are likely to invest in B, and 50% are likely to invest in C. Each portfolio has both stocks and bonds, and investors are equally likely to choose either.
This is a tree diagram that represents the probability of investors choosing the different financial products.
What is the probability of an investor choosing only bonds from portfolio B?

Respuesta :

Solution :

P(A) = 0.2

[tex]$P(B)=0.3$[/tex]

[tex]$P(C)=0.5$[/tex]

Each portfolio has both the stocks and the bonds, and the investors are equally likely to choose either of them.

Let Stock = S

      Bond  = b

Therefore, we have:

[tex]$P(S|A) = 0.5$[/tex]

[tex]$P(b|A) = 0.5$[/tex]

[tex]$P(S|B) = 0.5$[/tex]

[tex]$P(b|B) = 0.5$[/tex]

[tex]$P(S|C) = 0.5$[/tex]

[tex]$P(b|C) = 0.5$[/tex]

Therefore,

[tex]$P(b \text{ and } B)= P(b|B) \times P(B)$[/tex]

                    = 0.5 x 0.3

                    = 0.15

Ver imagen AbsorbingMan
mickymike92

Based on the tree diagram, probability of an investor choosing only bonds from portfolio B is 0.15.

What is probability?

Probability is the chance or likelihood of an event occurring.

Mathematically, probability is given as;

  • Probability = number of expected outcomes/number of possible outcomes

From the tree diagram:

P(A) = 0.2

P(B) = 0.3

P(C) = 0.5

The investors are equally likely to choose from each portfolio.

Each portfolio has both the stocks and the bonds.

Assuming stock = S and Bond = B.

Then;

P(S|A) = 0.5

P(b|A) = 0.5

P(S|B) = 0.5

P(b|B) = 0.5

P(S|C) = 0.5

P(b|C) = 0.5

[tex]P(b \text{ and } B)= P(b|B) \times P(B)[/tex]

[tex]P(b \text{ and } B)= 0.5 \times 0.3 = 0.15[/tex]

Therefore, the probability of an investor choosing only bonds from portfolio B is 0.15.

Learn more about probability at: https://brainly.com/question/251701

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